Question

The streptococci bacteria population N at time t (in months) is given by N = N0e
2t where N0 is the initial population. If the initial population was 100, how long does it take for the population to reach one million?

Answer 1

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Answer 2

SOLUTION

GIVEN

The streptococci bacteria population N at time t (in months) is given by

$\sf N = N_0 \: {e}^{2t}$

$\sf \: where \: N_0 \: is \: the \: initial \: population$

TO DETERMINE l

f the initial population was 100, how long does it take for the population to reach one million?

EVALUATION

Here it is given that the streptococci bacteria population N at time t is given by

$\sf N = N_0 \: {e}^{2t}$

Now from the given

$\sf N_0 = 100$

Let t months is required when N = 1,000,000

Thus we have

$\sf 1000000= 100 \: {e}^{2t}$

$\sf \implies {e}^{2t} = 10000$

Taking logarithm in both sides we get

$\sf \implies 2t=ln \: 10000$

$\sf \implies 2t \approx \: 9.2$

$\sf \implies t \approx \: 4.6$

FINAL ANSWER

Hence the required time = 4.6 months

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